Counterfactual Donkeys Dont Get High Mike Deigan Yale University - - PowerPoint PPT Presentation

Counterfactual Donkeys Don’t Get High

Mike Deigan Yale University SuB22, Potsdam

New Data

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New Data

Suppose Allie and Bert think Mary the potter probably didn’t make anything yesterday.

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New Data

Suppose Allie and Bert think Mary the potter probably didn’t make anything yesterday. (1) Allie:

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New Data

Suppose Allie and Bert think Mary the potter probably didn’t make anything yesterday. (1) Allie: If Mary had made a vase, she would have made it from glass.

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New Data

Suppose Allie and Bert think Mary the potter probably didn’t make anything yesterday. (1) Allie: If Mary had made a vase, she would have made it from glass. Case 1:

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New Data

Suppose Allie and Bert think Mary the potter probably didn’t make anything yesterday. (1) Allie: If Mary had made a vase, she would have made it from glass. Case 1: Mary actually made two vases, both from glass.

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New Data

Suppose Allie and Bert think Mary the potter probably didn’t make anything yesterday. (1) Allie: If Mary had made a vase, she would have made it from glass. ✓ Case 1: Mary actually made two vases, both from glass.

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New Data

Suppose Allie and Bert think Mary the potter probably didn’t make anything yesterday. (1) Allie: If Mary had made a vase, she would have made it from glass. ✓ Case 1: Mary actually made two vases, both from glass. (2) Bert: But she could have made a clay vase

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New Data

Suppose Allie and Bert think Mary the potter probably didn’t make anything yesterday. (1) Allie: If Mary had made a vase, she would have made it from glass. ✓ Case 1: Mary actually made two vases, both from glass. (2) Bert: But she could have made a clay vase (and she wouldn’t have made that from glass)!

1 / 40

New Data

Suppose Allie and Bert think Mary the potter probably didn’t make anything yesterday. (1) Allie: If Mary had made a vase, she would have made it from glass. ✓ Case 1: Mary actually made two vases, both from glass. (2) Bert: But she could have made a clay vase (and she wouldn’t have made that from glass)! Judgements: (1) ✓ (2) ??

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New Data

Suppose Allie and Bert think Mary the potter probably didn’t make anything yesterday. (1) Allie: If Mary had made a vase, she would have made it from glass. Case 2:

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New Data

Suppose Allie and Bert think Mary the potter probably didn’t make anything yesterday. (1) Allie: If Mary had made a vase, she would have made it from glass. Case 2: Mary did not make any vases.

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New Data

Suppose Allie and Bert think Mary the potter probably didn’t make anything yesterday. (1) Allie: If Mary had made a vase, she would have made it from glass. Case 2: Mary did not make any vases. (2) Bert: But she could have made a clay vase (and she wouldn’t have made that from glass)!

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New Data

Suppose Allie and Bert think Mary the potter probably didn’t make anything yesterday. (1) Allie: If Mary had made a vase, she would have made it from glass. ✗ Case 2: Mary did not make any vases. (2) Bert: But she could have made a clay vase (and she wouldn’t have made that from glass)!

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New Data

Suppose Allie and Bert think Mary the potter probably didn’t make anything yesterday. (1) Allie: If Mary had made a vase, she would have made it from glass. ✗ Case 2: Mary did not make any vases. (2) Bert: But she could have made a clay vase (and she wouldn’t have made that from glass)! Judgements: (1) ✗ (2) ✓

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New Data - Summary

(1) Allie: If Mary had made a vase, she would have made it from glass. (2) Bert: But she could have made a clay vase (and she wouldn’t have made that from glass)! Case 1: Mary made two glass vases. Case 2: Mary did not make any vases. Case 1 Case 2 (1) ✓ ✗ (2) ?? ✓

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So what?

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Old Data

(3) If Balaam owned a donkey, he would beat it.

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Old Data

(3) If Balaam owned a donkey, he would beat it. Apparent entailments: (4) a. If Herbert were a donkey Balaam owned, Balaam would beat Herbert.

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Old Data

(3) If Balaam owned a donkey, he would beat it. Apparent entailments: (4) a. If Herbert were a donkey Balaam owned, Balaam would beat Herbert. b. If Eeyore were a donkey Balaam owned, Balaam would beat Eeyore.

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Old Data

(3) If Balaam owned a donkey, he would beat it. Apparent entailments: (4) a. If Herbert were a donkey Balaam owned, Balaam would beat Herbert. b. If Eeyore were a donkey Balaam owned, Balaam would beat Eeyore. c. If Platero were a donkey Balaam owned, Balaam would beat Platero.

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Old Data - Two Accounts

Two routes to accounting for universal entailments:

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Old Data - Two Accounts

Two routes to accounting for universal entailments:

• 1. let a special property of the closeness ordering do the work

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Old Data - Two Accounts

Two routes to accounting for universal entailments:

• 1. let a special property of the closeness ordering do the work

(Walker and Romero (2015) on behalf of Wang (2009))

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Old Data - Two Accounts

Two routes to accounting for universal entailments:

• 1. let a special property of the closeness ordering do the work

(Walker and Romero (2015) on behalf of Wang (2009))

• 2. bake in universality semantically with a ‘high’ reading

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Old Data - Two Accounts

Two routes to accounting for universal entailments:

• 1. let a special property of the closeness ordering do the work

(Walker and Romero (2015) on behalf of Wang (2009))

• 2. bake in universality semantically with a ‘high’ reading
• n which

∃x[Px] Qx ⇔ ∀x[Px Qx]

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Old Data - Two Accounts

Two routes to accounting for universal entailments:

• 1. let a special property of the closeness ordering do the work

(Walker and Romero (2015) on behalf of Wang (2009))

• 2. bake in universality semantically with a ‘high’ reading
• n which

∃x[Px] Qx ⇔ ∀x[Px Qx]

(van Rooij (2006), Walker and Romero (2015))

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Thesis

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Thesis We should take Route 1.

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Thesis We should take Route 1.

The special ordering-based accounts predict the new data.

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Thesis We should take Route 1.

The special ordering-based accounts predict the new data. High reading accounts don’t.

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In other words. . . Counterfactual donkeys

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In other words. . . Counterfactual donkeys don’t get high.

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Overview

Accounting for the Old Data Ordering Semantics + Dynamic Binding Route 1: Special Orderings Route 2: High Readings Returning to the New Data The Problem for High Readings The Success of Special Orderings Some Objections and Replies Saving High Readings? Problem for Special Orderings? Takeaway

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Overview

Accounting for the Old Data Ordering Semantics + Dynamic Binding Route 1: Special Orderings Route 2: High Readings Returning to the New Data The Problem for High Readings The Success of Special Orderings Some Objections and Replies Saving High Readings? Problem for Special Orderings? Takeaway

Ordering Semantics + Dynamic Binding

Familiar Stalnaker-Lewis style semantics.

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Ordering Semantics + Dynamic Binding

Familiar Stalnaker-Lewis style semantics. Selection function: (5) f(A, w) = {w′ : w ∈ A ∧ ¬∃w′′(w′′ ∈ A ∧ w′′ <w w′)} The A-worlds nearest to w, according to <w.

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Ordering Semantics + Dynamic Binding

Familiar Stalnaker-Lewis style semantics. Selection function: (5) f(A, w) = {w′ : w ∈ A ∧ ¬∃w′′(w′′ ∈ A ∧ w′′ <w w′)} The A-worlds nearest to w, according to <w. (6) A C = {w : ∀w′(w′ ∈ f(A, w) ⊃ w ∈ C)} C is true at all the nearest A-worlds.

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Ordering Semantics + Dynamic Binding

DPL with possible worlds (based on Groenendijk and Stokhof (1991) and Groenendijk, Stokhof, and Veltman (1996))

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Ordering Semantics + Dynamic Binding

DPL with possible worlds (based on Groenendijk and Stokhof (1991) and Groenendijk, Stokhof, and Veltman (1996)) possibility: world, assignment info state s: set of possibilities update function [·] from a state and sentence to a state

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Ordering Semantics + Dynamic Binding

DPL with possible worlds (based on Groenendijk and Stokhof (1991) and Groenendijk, Stokhof, and Veltman (1996)) possibility: world, assignment info state s: set of possibilities update function [·] from a state and sentence to a state (7) a. s[F(x)] = {i : i ∈ s ∧ wi ∈ F(gi(x))}

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Ordering Semantics + Dynamic Binding

DPL with possible worlds (based on Groenendijk and Stokhof (1991) and Groenendijk, Stokhof, and Veltman (1996)) possibility: world, assignment info state s: set of possibilities update function [·] from a state and sentence to a state (7) a. s[F(x)] = {i : i ∈ s ∧ wi ∈ F(gi(x))} b. s[∃x] = {i : ∃j∃d(j ∈ s ∧ d ∈ D ∧ wi = wj ∧ gi = gx→d

j

)}

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Ordering Semantics + Dynamic Binding

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Ordering Semantics + Dynamic Binding

j is an A-possibility for i (or j ∈ /A/i) iff ∃k(gk = gi ∧ j ∈ {k}[A]).

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Ordering Semantics + Dynamic Binding

j is an A-possibility for i (or j ∈ /A/i) iff ∃k(gk = gi ∧ j ∈ {k}[A]). Selection function: (8) f(A, i) = {j : j ∈ /A/i ∧ ¬∃k(k ∈ /A/i ∧ wk <wi wj)}. Finds the nearest A-possibility, where possibilities are ordered by their worlds.

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Ordering Semantics + Dynamic Binding

j is an A-possibility for i (or j ∈ /A/i) iff ∃k(gk = gi ∧ j ∈ {k}[A]). Selection function: (8) f(A, i) = {j : j ∈ /A/i ∧ ¬∃k(k ∈ /A/i ∧ wk <wi wj)}. Finds the nearest A-possibility, where possibilities are ordered by their worlds. (9) s[A C] = {i : i ∈ s ∧ ∀j(j ∈ f(A, i) ⊃ {j}[C] ∅)} C is verified by all selected possibilities

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Ordering Semantics + Dynamic Binding

(3) If Balaam owned a donkey, he would beat it.

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Ordering Semantics + Dynamic Binding

(3) If Balaam owned a donkey, he would beat it. (10) ∃xDBO(x) BB(x)

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Dynamic Binding + Ordering Semantics

w0

Dynamic Binding + Ordering Semantics

w0 ¬DBO DBO DBO = donkey that Balaam owns

Dynamic Binding + Ordering Semantics

w0 ¬DBO DBO BB ¬BB DBO = donkey that Balaam owns BB = thing that Balaam beats

Dynamic Binding + Ordering Semantics

w0 ¬DBO DBO BB ¬BB

• h
• e
• p

DBO = donkey that Balaam owns BB = thing that Balaam beats e = Eeyore h = Herbert p = Platero

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w0

¬DBO DBO BB ¬BB

• h
• e
• p

w0

¬DBO DBO BB ¬BB

• h
• e
• p

∨

w1

BB ¬BB

w0

¬DBO DBO BB ¬BB

• h
• e
• p

∨

w1

BB ¬BB

• h
• e
• p

w0

¬DBO DBO BB ¬BB

• h
• e
• p

∨

w1

BB ¬BB

• h
• e
• p

∨

w2

BB ¬BB

• h
• e
• p

w0

¬DBO DBO BB ¬BB

• h
• e
• p

∨

w1

BB ¬BB

• h
• e
• p

∨

w2

BB ¬BB

• h
• e
• p

∨

w3

BB ¬BB

• h
• e
• p

w0

¬DBO DBO BB ¬BB

• h
• e
• p

∨

w1

BB ¬BB

• h
• e
• p

∨

w2

BB ¬BB

• h
• e
• p

∨

w3

BB ¬BB

• h
• e
• p

w0, gx→h w0, gx→e w0, gx→p

w0

¬DBO DBO BB ¬BB

• h
• e
• p

∨

w1

BB ¬BB

• h
• e
• p

∨

w2

BB ¬BB

• h
• e
• p

∨

w3

BB ¬BB

• h
• e
• p

w0, gx→h w0, gx→e w0, gx→p w1, gx→h w1, gx→e w1, gx→p w2, gx→h w2, gx→e w2, gx→p w3, gx→h w3, gx→e w3, gx→p

w0

¬DBO DBO BB ¬BB

• h
• e
• p

∨

w1

BB ¬BB

• h
• e
• p

∨

w2

BB ¬BB

• h
• e
• p

∨

w3

BB ¬BB

• h
• e
• p

w0, gx→h w0, gx→e w0, gx→p w1, gx→h w1, gx→e w1, gx→p w2, gx→h w2, gx→e w2, gx→p w3, gx→h w3, gx→e w3, gx→p = = = = = = = =

w0

¬DBO DBO BB ¬BB

• h
• e
• p

∨

w1

BB ¬BB

• h
• e
• p

∨

w2

BB ¬BB

• h
• e
• p

∨

w3

BB ¬BB

• h
• e
• p

w0, gx→h w0, gx→e w0, gx→p w1, gx→h w1, gx→e w1, gx→p w2, gx→h w2, gx→e w2, gx→p w3, gx→h w3, gx→e w3, gx→p = = = = = = = = ∨ ∨ ∨

w0

¬DBO DBO BB ¬BB

• h
• e
• p

∨

w1

BB ¬BB

• h
• e
• p

∨

w2

BB ¬BB

• h
• e
• p

∨

w3

BB ¬BB

• h
• e
• p

w0, gx→h w0, gx→e w0, gx→p w1, gx→h w1, gx→e w1, gx→p w2, gx→h w2, gx→e w2, gx→p w3, gx→h w3, gx→e w3, gx→p = = = = = = = = ∨ ∨ ∨

w0

¬DBO DBO BB ¬BB

• h
• e
• p

∨

w1

BB ¬BB

• h
• e
• p

∨

w2

BB ¬BB

• h
• e
• p

∨

w3

BB ¬BB

• h
• e
• p

w0, gx→h w0, gx→e w0, gx→p w1, gx→h w1, gx→e w1, gx→p w2, gx→h w2, gx→e w2, gx→p w3, gx→h w3, gx→e w3, gx→p = = = = = = = = ∨ ∨ ∨

w0

¬DBO DBO BB ¬BB

• h
• e
• p

∨

w1

BB ¬BB

• h
• e
• p

∨

w2

BB ¬BB

• h
• e
• p

∨

w3

BB ¬BB

• h
• e
• p

w0, gx→h w0, gx→e w0, gx→p w1, gx→h w1, gx→e w1, gx→p w2, gx→h w2, gx→e w2, gx→p w3, gx→h w3, gx→e w3, gx→p = = = = = = = = ∨ ∨ ∨

w0

¬DBO DBO BB ¬BB

• h
• e
• p

∨

w1

BB ¬BB

• h
• e
• p

∨

w2

BB ¬BB

• h
• e
• p

∨

w3

BB ¬BB

• h
• e
• p

w0, gx→h w0, gx→e w0, gx→p w1, gx→h w1, gx→e w1, gx→p w2, gx→h w2, gx→e w2, gx→p w3, gx→h w3, gx→e w3, gx→p = = = = = = = = ∨ ∨ ∨

14 / 40

DBO ¬BB

w1

¬DBO DBO BB ¬BB

• h
• e
• p

w3

w1, gx→h w3, gx→p

DBO ¬BB

w1

¬DBO DBO BB ¬BB

• h
• e
• p

w3

w1, gx→h w3, gx→p

∃xDBO(x) BB(x)

DBO ¬BB

w1

¬DBO DBO BB ¬BB

• h
• e
• p

w3

w1, gx→h w3, gx→p

∃xDBO(x) BB(x) ∀j(j ∈ f(A, i){j}[BB(x)] ∅

DBO ¬BB

w1

¬DBO DBO BB ¬BB

• h
• e
• p

w3

w1, gx→h w3, gx→p

∃xDBO(x) BB(x) ∀j(j ∈ f(A, i){j}[BB(x)] ∅

{w1, gx→h}[BB(x)]

DBO ¬BB

w1

¬DBO DBO BB ¬BB

• h
• e
• p

w3

w1, gx→h w3, gx→p

∃xDBO(x) BB(x) ∀j(j ∈ f(A, i){j}[BB(x)] ∅

{w1, gx→h}[BB(x)] w1 ∈ BB(h)?

DBO ¬BB

w1

¬DBO DBO BB ¬BB

• h
• e
• p

w3

w1, gx→h w3, gx→p

∃xDBO(x) BB(x) ∀j(j ∈ f(A, i){j}[BB(x)] ∅

{w1, gx→h}[BB(x)] w1 ∈ BB(h)? ✓

DBO ¬BB

w1

¬DBO DBO BB ¬BB

• h
• e
• p

w3

w1, gx→h w3, gx→p

∃xDBO(x) BB(x) ∀j(j ∈ f(A, i){j}[BB(x)] ∅

{w1, gx→h}[BB(x)] w1 ∈ BB(h)? ✓ = {w1, gx→h} ∅

DBO ¬BB

w1

¬DBO DBO BB ¬BB

• h
• e
• p

w3

w1, gx→h w3, gx→p

∃xDBO(x) BB(x) ∀j(j ∈ f(A, i){j}[BB(x)] ∅

{w1, gx→h}[BB(x)] w1 ∈ BB(h)? ✓ = {w1, gx→h} ∅

✓

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Ordering Semantics + Dynamic Binding

Problem: no universal entailments

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Ordering Semantics + Dynamic Binding

Problem: no universal entailments (11) If Balaam owned a donkey, he would beat it. (12) a. If Herbert were a donkey Balaam owned, Balaam would beat Herbert. b. If Eeyore were a donkey Balaam owned, Balaam would beat Eeyore. c. If Platero were a donkey Balaam owned, Balaam would beat Platero.

16 / 40

Ordering Semantics + Dynamic Binding

Problem: no universal entailments (11) If Balaam owned a donkey, he would beat it. (12) a. If Herbert were a donkey Balaam owned, Balaam would beat Herbert. b. If Eeyore were a donkey Balaam owned, Balaam would beat Eeyore. c. If Platero were a donkey Balaam owned, Balaam would beat Platero.

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Ordering Semantics + Dynamic Binding

(12-b) If Eeyore were a donkey Balaam owned, Balaam would beat Eeyore. (13) DBO(e) BB(e)

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w0

¬DBO DBO BB ¬BB

• h
• e
• p

∨

w1

BB ¬BB

• h
• e
• p

∨

w2

BB ¬BB

• h
• e
• p

∨

w3

BB ¬BB

• h
• e
• p

w0, gx→h w0, gx→e w0, gx→p w1, gx→h w1, gx→e w1, gx→p w2, gx→h w2, gx→e w2, gx→p w3, gx→h w3, gx→e w3, gx→p = = = = = = = = ∨ ∨ ∨

w0

¬DBO DBO BB ¬BB

• h
• e
• p

∨

w1

BB ¬BB

• h
• e
• p

∨

w2

BB ¬BB

• h
• e
• p

∨

w3

BB ¬BB

• h
• e
• p

w0, gx→h w0, gx→e w0, gx→p w1, gx→h w1, gx→e w1, gx→p w2, gx→h w2, gx→e w2, gx→p w3, gx→h w3, gx→e w3, gx→p = = = = = = = = ∨ ∨ ∨

w0

¬DBO DBO BB ¬BB

• h
• e
• p

∨

w1

BB ¬BB

• h
• e
• p

∨

w2

BB ¬BB

• h
• e
• p

∨

w3

BB ¬BB

• h
• e
• p

w0, gx→h w0, gx→e w0, gx→p w1, gx→h w1, gx→e w1, gx→p w2, gx→h w2, gx→e w2, gx→p w3, gx→h w3, gx→e w3, gx→p = = = = = = = = ∨ ∨ ∨

18 / 40

DBO ¬BB

w2

¬DBO DBO BB ¬BB

• h
• e
• p

w3

w1, gx→p w2, gx→h w2, gx→e w2, gx→p

DBO ¬BB

w2

¬DBO DBO BB ¬BB

• h
• e
• p

w3

w1, gx→p w2, gx→h w2, gx→e w2, gx→p

DBO(e) BB(e)

DBO ¬BB

w2

¬DBO DBO BB ¬BB

• h
• e
• p

w3

w1, gx→p w2, gx→h w2, gx→e w2, gx→p

DBO(e) BB(e) ∀j(j ∈ f(A, i){j}[BB(e)] ∅

DBO ¬BB

w2

¬DBO DBO BB ¬BB

• h
• e
• p

w3

w1, gx→p w2, gx→h w2, gx→e w2, gx→p

DBO(e) BB(e) ∀j(j ∈ f(A, i){j}[BB(e)] ∅

w2 ∈ BB(e)?

DBO ¬BB

w2

¬DBO DBO BB ¬BB

• h
• e
• p

w3

w1, gx→p w2, gx→h w2, gx→e w2, gx→p

DBO(e) BB(e) ∀j(j ∈ f(A, i){j}[BB(e)] ∅

w2 ∈ BB(e)? ✗

DBO ¬BB

w2

¬DBO DBO BB ¬BB

• h
• e
• p

w3

w1, gx→p w2, gx→h w2, gx→e w2, gx→p

DBO(e) BB(e) ∀j(j ∈ f(A, i){j}[BB(e)] ∅

w2 ∈ BB(e)? ✗

✗

19 / 40

Ordering Semantics + Dynamic Binding

Problem: no universal entailments (14) If Balaam owned a donkey, he would beat it. (15) a. If Herbert were a donkey Balaam owned, Balaam would beat Herbert. b. If Eeyore were a donkey Balaam owned, Balaam would beat Eeyore. c. If Platero were a donkey Balaam owned, Balaam would beat Platero.

20 / 40

Ordering Semantics + Dynamic Binding

Problem: no universal entailments (14) If Balaam owned a donkey, he would beat it. (15) a. If Herbert were a donkey Balaam owned, Balaam would beat Herbert. b. If Eeyore were a donkey Balaam owned, Balaam would beat Eeyore. c. If Platero were a donkey Balaam owned, Balaam would beat Platero. How to fix this?

20 / 40

Ordering Semantics + Dynamic Binding

Problem: no universal entailments (14) If Balaam owned a donkey, he would beat it. (15) a. If Herbert were a donkey Balaam owned, Balaam would beat Herbert. b. If Eeyore were a donkey Balaam owned, Balaam would beat Eeyore. c. If Platero were a donkey Balaam owned, Balaam would beat Platero. How to fix this? Route 1: special orderings Route 2: high readings

20 / 40

Route 1: Special Orderings

Walker and Romero (2015): universal entailments would follow from A C iff the closeness ordering were such that

21 / 40

Route 1: Special Orderings

Walker and Romero (2015): universal entailments would follow from A C iff the closeness ordering were such that for any a, b ∈ D, the closest world which combines with gx→a to form an A-possibility is as close as the closest world which combines with gx→b to form an A-possibility.

21 / 40

Route 1: Special Orderings

Walker and Romero (2015): universal entailments would follow from A C iff the closeness ordering were such that for any a, b ∈ D, the closest world which combines with gx→a to form an A-possibility is as close as the closest world which combines with gx→b to form an A-possibility. An ordering set S is special relative to a state s and sentence A iff (16) ∀i(i ∈ s ⊃ ∀j(j ∈ /A/i ⊃ ∃k(k ∈ f(A, i) ∧ gj = gk))) For all possibilities i in s, if j is an A-possibility for i, then among the nearest (relative to i) A-possibilities is a possibility which shares an assigment with j.

21 / 40

w0

¬DBO DBO BB ¬BB

• h
• e
• p

∨

w1

BB ¬BB

• h
• e
• p

∨

w2

BB ¬BB

• h
• e
• p

∨

w3

BB ¬BB

• h
• e
• p

w3, gx→p

w0

¬DBO DBO BB ¬BB

• h
• e
• p

∨

w1

BB ¬BB

• h
• e
• p

∨

w2

BB ¬BB

• h
• e
• p

∨

w3

BB ¬BB

• h
• e
• p

w3, gx→p

w0

¬DBO DBO BB ¬BB

• h
• e
• p

∨

w1

BB ¬BB

• h
• e
• p

∨

w2

BB ¬BB

• h
• e
• p

∨

w3

BB ¬BB

• h
• e
• p

w3, gx→p

w0

¬DBO DBO BB ¬BB

• h
• e
• p

∨

w1

BB ¬BB

• h
• e
• p

∨

w2

BB ¬BB

• h
• e
• p

∨

w3

BB ¬BB

• h
• e
• p

w3, gx→p

22 / 40

w0

¬DBO DBO BB ¬BB

• h
• e
• p

∨

w1

BB ¬BB

• h
• e
• p

=

w2

BB ¬BB

• h
• e
• p

=

w3

BB ¬BB

• h
• e
• p

w0, gx→h w0, gx→e w0, gx→p w1, gx→h w1, gx→e w1, gx→p w2, gx→h w2, gx→e w2, gx→p w3, gx→h w3, gx→e w3, gx→p = = = = = = = = ∨ = =

w0

¬DBO DBO BB ¬BB

• h
• e
• p

∨

w1

BB ¬BB

• h
• e
• p

=

w2

BB ¬BB

• h
• e
• p

=

w3

BB ¬BB

• h
• e
• p

w0, gx→h w0, gx→e w0, gx→p w1, gx→h w1, gx→e w1, gx→p w2, gx→h w2, gx→e w2, gx→p w3, gx→h w3, gx→e w3, gx→p = = = = = = = = ∨ = =

w0

¬DBO DBO BB ¬BB

• h
• e
• p

∨

w1

BB ¬BB

• h
• e
• p

=

w2

BB ¬BB

• h
• e
• p

=

w3

BB ¬BB

• h
• e
• p

w0, gx→h w0, gx→e w0, gx→p w1, gx→h w1, gx→e w1, gx→p w2, gx→h w2, gx→e w2, gx→p w3, gx→h w3, gx→e w3, gx→p = = = = = = = = ∨ = =

23 / 40

w1

¬DBO DBO BB ¬BB

• h
• e
• p

DBO ¬BB

=

w2

BB ¬BB

• h
• e
• p

=

w3

BB ¬BB

• h
• e
• p

w1, gx→h w2, gx→e w3, gx→p

w1

¬DBO DBO BB ¬BB

• h
• e
• p

DBO ¬BB

=

w2

BB ¬BB

• h
• e
• p

=

w3

BB ¬BB

• h
• e
• p

w1, gx→h w2, gx→e w3, gx→p

∃xDBO(x) BB(x)

w1

¬DBO DBO BB ¬BB

• h
• e
• p

DBO ¬BB

=

w2

BB ¬BB

• h
• e
• p

=

w3

BB ¬BB

• h
• e
• p

w1, gx→h w2, gx→e w3, gx→p

∃xDBO(x) BB(x) ✗

24 / 40

Route 2: High Readings

Leave world ordering ≤ alone,

25 / 40

Route 2: High Readings

Leave world ordering ≤ alone, but define an assignment-sensitive similarity ordering ≤∗ based on it. (17) j ≤∗

i k iff wj ≤wi wk ∧ gj = gk

25 / 40

Route 2: High Readings

Leave world ordering ≤ alone, but define an assignment-sensitive similarity ordering ≤∗ based on it. (17) j ≤∗

i k iff wj ≤wi wk ∧ gj = gk

(18) f ∗(A, i) = {j : j ∈ /A/i ∧ ¬∃k(k ∈ /A/i ∧ k <∗

wi j)}.

(19) s[A C] = {i : i ∈ s ∧ ∀j(j ∈ f ∗(A, i) ⊃ {j}[C] ∅)}

25 / 40

w0

¬DBO DBO BB ¬BB

• h
• e
• p

∨

w1

BB ¬BB

• h
• e
• p

∨

w2

BB ¬BB

• h
• e
• p

∨

w3

BB ¬BB

• h
• e
• p

w0

¬DBO DBO BB ¬BB

• h
• e
• p

∨

w1

BB ¬BB

• h
• e
• p

∨

w2

BB ¬BB

• h
• e
• p

∨

w3

BB ¬BB

• h
• e
• p

w0, gx→h w0, gx→e w0, gx→p w1, gx→h w1, gx→e w1, gx→p w2, gx→h w2, gx→e w2, gx→p w3, gx→h w3, gx→e w3, gx→p

w0

¬DBO DBO BB ¬BB

• h
• e
• p

∨

w1

BB ¬BB

• h
• e
• p

∨

w2

BB ¬BB

• h
• e
• p

∨

w3

BB ¬BB

• h
• e
• p

w0, gx→h w0, gx→e w0, gx→p w1, gx→h w1, gx→e w1, gx→p w2, gx→h w2, gx→e w2, gx→p w3, gx→h w3, gx→e w3, gx→p

w0

¬DBO DBO BB ¬BB

• h
• e
• p

∨

w1

BB ¬BB

• h
• e
• p

∨

w2

BB ¬BB

• h
• e
• p

∨

w3

BB ¬BB

• h
• e
• p

w0, gx→h w0, gx→e w0, gx→p w1, gx→h w1, gx→e w1, gx→p w2, gx→h w2, gx→e w2, gx→p w3, gx→h w3, gx→e w3, gx→p

w0

¬DBO DBO BB ¬BB

• h
• e
• p

∨

w1

BB ¬BB

• h
• e
• p

∨

w2

BB ¬BB

• h
• e
• p

∨

w3

BB ¬BB

• h
• e
• p

w0, gx→h w0, gx→e w0, gx→p w1, gx→h w1, gx→e w1, gx→p w2, gx→h w2, gx→e w2, gx→p w3, gx→h w3, gx→e w3, gx→p

• <∗

<∗ <∗ <∗ <∗ <∗ <∗ <∗ <∗

w0

¬DBO DBO BB ¬BB

• h
• e
• p

∨

w1

BB ¬BB

• h
• e
• p

∨

w2

BB ¬BB

• h
• e
• p

∨

w3

BB ¬BB

• h
• e
• p

w0, gx→h w0, gx→e w0, gx→p w1, gx→h w1, gx→e w1, gx→p w2, gx→h w2, gx→e w2, gx→p w3, gx→h w3, gx→e w3, gx→p

• <∗

<∗ <∗ <∗ <∗ <∗ <∗ <∗ <∗

w0

¬DBO DBO BB ¬BB

• h
• e
• p

∨

w1

BB ¬BB

• h
• e
• p

∨

w2

BB ¬BB

• h
• e
• p

∨

w3

BB ¬BB

• h
• e
• p

w0, gx→h w0, gx→e w0, gx→p w1, gx→h w1, gx→e w1, gx→p w2, gx→h w2, gx→e w2, gx→p w3, gx→h w3, gx→e w3, gx→p

• <∗

<∗ <∗ <∗ <∗ <∗ <∗ <∗ <∗

w0

¬DBO DBO BB ¬BB

• h
• e
• p

∨

w1

BB ¬BB

• h
• e
• p

∨

w2

BB ¬BB

• h
• e
• p

∨

w3

BB ¬BB

• h
• e
• p

w0, gx→h w0, gx→e w0, gx→p w1, gx→h w1, gx→e w1, gx→p w2, gx→h w2, gx→e w2, gx→p w3, gx→h w3, gx→e w3, gx→p

• <∗

<∗ <∗ <∗ <∗ <∗ <∗ <∗ <∗

w0

¬DBO DBO BB ¬BB

• h
• e
• p

∨

w1

BB ¬BB

• h
• e
• p

∨

w2

BB ¬BB

• h
• e
• p

∨

w3

BB ¬BB

• h
• e
• p

w0, gx→h w0, gx→e w0, gx→p w1, gx→h w1, gx→e w1, gx→p w2, gx→h w2, gx→e w2, gx→p w3, gx→h w3, gx→e w3, gx→p

• <∗

<∗ <∗ <∗ <∗ <∗ <∗ <∗ <∗

26 / 40

w1

¬DBO DBO BB ¬BB

• h
• e
• p

DBO ¬BB

∨

w2

BB ¬BB

• h
• e
• p

∨

w3

BB ¬BB

• h
• e
• p

w1, gx→h w2, gx→e w3, gx→p

w1

¬DBO DBO BB ¬BB

• h
• e
• p

DBO ¬BB

∨

w2

BB ¬BB

• h
• e
• p

∨

w3

BB ¬BB

• h
• e
• p

w1, gx→h w2, gx→e w3, gx→p

∃xDBO(x) BB(x)

w1

¬DBO DBO BB ¬BB

• h
• e
• p

DBO ¬BB

∨

w2

BB ¬BB

• h
• e
• p

∨

w3

BB ¬BB

• h
• e
• p

w1, gx→h w2, gx→e w3, gx→p

∃xDBO(x) BB(x)

w1

¬DBO DBO BB ¬BB

• h
• e
• p

DBO ¬BB

∨

w2

BB ¬BB

• h
• e
• p

∨

w3

BB ¬BB

• h
• e
• p

w1, gx→h w2, gx→e w3, gx→p

∃xDBO(x) BB(x) ✗

27 / 40

Overview

Accounting for the Old Data Ordering Semantics + Dynamic Binding Route 1: Special Orderings Route 2: High Readings Returning to the New Data The Problem for High Readings The Success of Special Orderings Some Objections and Replies Saving High Readings? Problem for Special Orderings? Takeaway

New Data - Summary

(1) Allie: If Mary had made a vase, she would have made it from glass. (2) Bert: But she could have made a clay vase (and she wouldn’t have made that from glass)! Case 1: Mary made two glass vases. Case 2: Mary did not make any vases. Case 1 Case 2 (1) ✓ ✗ (2) ?? ✓

28 / 40

Problem for High Readings

w0

¬VMM VMM G ¬G

• g1
• g2

Problem for High Readings

w0

¬VMM VMM G ¬G

• g1
• g2

∨

w1

G ¬G

Problem for High Readings

w0

¬VMM VMM G ¬G

• g1
• g2

∨

w1

G ¬G

• g1
• g2
• c

Problem for High Readings

w0

¬VMM VMM G ¬G

• g1
• g2

∨

w1

G ¬G

• g1
• g2
• c

w0, gx→g1 w0, gx→g2 w0, gx→c

Problem for High Readings

w0

¬VMM VMM G ¬G

• g1
• g2

∨

w1

G ¬G

• g1
• g2
• c

w0, gx→g1 w0, gx→g2 w0, gx→c w1, gx→g1 w1, gx→g2 w1, gx→c

Problem for High Readings

w0

¬VMM VMM G ¬G

• g1
• g2

∨

w1

G ¬G

• g1
• g2
• c

w0, gx→g1 w0, gx→g2 w0, gx→c w1, gx→g1 w1, gx→g2 w1, gx→c

Problem for High Readings

w0

¬VMM VMM G ¬G

• g1
• g2

∨

w1

G ¬G

• g1
• g2
• c

w0, gx→g1 w0, gx→g2 w0, gx→c w1, gx→g1 w1, gx→g2 w1, gx→c

• <∗

<∗ <∗

Problem for High Readings

w0

¬VMM VMM G ¬G

• g1
• g2

∨

w1

G ¬G

• g1
• g2
• c

w0, gx→g1 w0, gx→g2 w0, gx→c w1, gx→g1 w1, gx→g2 w1, gx→c

• <∗

<∗ <∗ ∃xVMM(x) G(x)

Problem for High Readings

w0

¬VMM VMM G ¬G

• g1
• g2

∨

w1

G ¬G

• g1
• g2
• c

w0, gx→g1 w0, gx→g2 w0, gx→c w1, gx→g1 w1, gx→g2 w1, gx→c

• <∗

<∗ <∗ ∃xVMM(x) G(x)

Problem for High Readings

w0

¬VMM VMM G ¬G

• g1
• g2

∨

w1

G ¬G

• g1
• g2
• c

w0, gx→g1 w0, gx→g2 w0, gx→c w1, gx→g1 w1, gx→g2 w1, gx→c

• <∗

<∗ <∗ ∃xVMM(x) G(x)

Problem for High Readings

w0

¬VMM VMM G ¬G

• g1
• g2

∨

w1

G ¬G

• g1
• g2
• c

w0, gx→g1 w0, gx→g2 w0, gx→c w1, gx→g1 w1, gx→g2 w1, gx→c

• <∗

<∗ <∗ ∃xVMM(x) G(x)

Problem for High Readings

w0

¬VMM VMM G ¬G

• g1
• g2

∨

w1

G ¬G

• g1
• g2
• c

w0, gx→g1 w0, gx→g2 w0, gx→c w1, gx→g1 w1, gx→g2 w1, gx→c

• <∗

<∗ <∗ ∃xVMM(x) G(x)

Problem for High Readings

w0

¬VMM VMM G ¬G

• g1
• g2

∨

w1

G ¬G

• g1
• g2
• c

w0, gx→g1 w0, gx→g2 w0, gx→c w1, gx→g1 w1, gx→g2 w1, gx→c

• <∗

<∗ <∗ ∃xVMM(x) G(x)

Problem for High Readings

w0

¬VMM VMM G ¬G

• g1
• g2

∨

w1

G ¬G

• g1
• g2
• c

w0, gx→g1 w0, gx→g2 w0, gx→c w1, gx→g1 w1, gx→g2 w1, gx→c

• <∗

<∗ <∗ ∃xVMM(x) G(x)

Problem for High Readings

w0

¬VMM VMM G ¬G

• g1
• g2

∨

w1

G ¬G

• g1
• g2
• c

w0, gx→g1 w0, gx→g2 w0, gx→c w1, gx→g1 w1, gx→g2 w1, gx→c

• <∗

<∗ <∗ ∃xVMM(x) G(x) w1 ∈ G(c)?

Problem for High Readings

w0

¬VMM VMM G ¬G

• g1
• g2

∨

w1

G ¬G

• g1
• g2
• c

w0, gx→g1 w0, gx→g2 w0, gx→c w1, gx→g1 w1, gx→g2 w1, gx→c

• <∗

<∗ <∗ ∃xVMM(x) G(x) w1 ∈ G(c)? ✗

29 / 40

Success of Special Orderings

Assumption: ≤ is strongly centered: w0 <w0 w1

30 / 40

Success of Special Orderings

w0

¬VMM VMM G ¬G

• g1
• g2

Success of Special Orderings

w0

¬VMM VMM G ¬G

• g1
• g2

∨

w1

G ¬G

Success of Special Orderings

w0

¬VMM VMM G ¬G

• g1
• g2

∨

w1

G ¬G

• g1
• g2
• c

Success of Special Orderings

w0

¬VMM VMM G ¬G

• g1
• g2

∨

w1

G ¬G

• g1
• g2
• c

w1, gx→c

Success of Special Orderings

w0

¬VMM VMM G ¬G

• g1
• g2

∨

w1

G ¬G

• g1
• g2
• c

w1, gx→c

Success of Special Orderings

w0

¬VMM VMM G ¬G

• g1
• g2

∨

w1

G ¬G

• g1
• g2
• c

w1, gx→c ¬w0 <w0 w1

31 / 40

Success of Special Orderings

Assumption: ≤ is strongly centered: w0 <w0 w1

32 / 40

Success of Special Orderings

Assumption: ≤ is strongly centered: w0 <w0 w1 Result: no special order in Case 1.

32 / 40

Success of Special Orderings

Assumption: ≤ is strongly centered: w0 <w0 w1 Result: no special order in Case 1. No universal entailments for merely possible antecedent satisfiers.

32 / 40

Success of Special Orderings

Assumption: ≤ is strongly centered: w0 <w0 w1 Result: no special order in Case 1. No universal entailments for merely possible antecedent satisfiers. (Possibly) universal entailments for (1) in Case 2.

32 / 40

Success of Special Orderings

Assumption: ≤ is strongly centered: w0 <w0 w1 Result: no special order in Case 1. No universal entailments for merely possible antecedent satisfiers. (Possibly) universal entailments for (1) in Case 2. Right predictions about the new data.

32 / 40

Overview

Accounting for the Old Data Ordering Semantics + Dynamic Binding Route 1: Special Orderings Route 2: High Readings Returning to the New Data The Problem for High Readings The Success of Special Orderings Some Objections and Replies Saving High Readings? Problem for Special Orderings? Takeaway

Saving High Readings: Weak?

Objection: the high reading accounts have ways of dealing with weak/low readings as well. (20) a. If I had a dime, I would put it in the meter. b. If I had picked a number, I would have picked 3.

33 / 40

Saving High Readings: Weak?

Objection: the high reading accounts have ways of dealing with weak/low readings as well. (20) a. If I had a dime, I would put it in the meter. b. If I had picked a number, I would have picked 3. This vase case is just one of those.

33 / 40

Saving High Readings: Weak?

Objection: the high reading accounts have ways of dealing with weak/low readings as well. (20) a. If I had a dime, I would put it in the meter. b. If I had picked a number, I would have picked 3. This vase case is just one of those.

• No. Consider

Case 3: Mary made one glass vase and one clay vase.

33 / 40

Saving High Readings: Weak?

Objection: the high reading accounts have ways of dealing with weak/low readings as well. (20) a. If I had a dime, I would put it in the meter. b. If I had picked a number, I would have picked 3. This vase case is just one of those.

• No. Consider

Case 3: Mary made one glass vase and one clay vase. (1) false in this case, which is not what we’d expect on a weak/low reading.

33 / 40

Saving High Readings: QDR?

c in Case 1 gets ignored due to quantifier domain restriction.

34 / 40

Saving High Readings: QDR?

c in Case 1 gets ignored due to quantifier domain restriction. Maybe, but how can this get Case 2 right?

34 / 40

Saving High Readings: QDR?

c in Case 1 gets ignored due to quantifier domain restriction. Maybe, but how can this get Case 2 right? Shouldn’t the possible clay vase be irrelevant still?

34 / 40

Problem for Special Orderings?

35 / 40

Problem for Special Orderings?

Walker and Romero (2015): cases of universal entailments without special order.

35 / 40

Problem for Special Orderings?

Walker and Romero (2015): cases of universal entailments without special order. (21) Scenario: Balaam took part in a game show which had the following format. If you win the easy first round, you win Herbert, an obnoxious and disobedient

• donkey. The reward for the much more difficult second

and third rounds are the well-mannered and obedient donkeys Eeyore and Platero, respectively. Losing a round of the game eliminates the player, keeping them from advancing to any later rounds. Balaam was eliminated in the first round, and so remains donkeyless.

35 / 40

Problem for Special Orderings?

John, only aware of the game’s first round, asserts (22), since he knows about Balaam’s short temper. (22) If Balaam owned a donkey, he would beat it.

36 / 40

Problem for Special Orderings?

John, only aware of the game’s first round, asserts (22), since he knows about Balaam’s short temper. (22) If Balaam owned a donkey, he would beat it. Sarah, who has more information about the game, corrects him with (23). (23) No, Balaam could have won Platero or Eeyore too, and he wouldn’t beat either of them if he owned them.

36 / 40

Problem for Special Orderings?

John, only aware of the game’s first round, asserts (22), since he knows about Balaam’s short temper. (22) If Balaam owned a donkey, he would beat it. Sarah, who has more information about the game, corrects him with (23). (23) No, Balaam could have won Platero or Eeyore too, and he wouldn’t beat either of them if he owned them. Seems like Sarah is right, so there are universal entailments.

36 / 40

Problem for Special Orderings?

John, only aware of the game’s first round, asserts (22), since he knows about Balaam’s short temper. (22) If Balaam owned a donkey, he would beat it. Sarah, who has more information about the game, corrects him with (23). (23) No, Balaam could have won Platero or Eeyore too, and he wouldn’t beat either of them if he owned them. Seems like Sarah is right, so there are universal entailments. But intuitively, the world where Balaam wins only one round is more similar to the actual world than ones where he wins two

• r three. So no special order.

36 / 40

Problem for Special Orderings?

Response part 1:

37 / 40

Problem for Special Orderings?

Response part 1: closeness ordering need not correspond to intuitive ordering.

37 / 40

Problem for Special Orderings?

Response part 1: closeness ordering need not correspond to intuitive ordering. Recall Fine (1975): (24) a. If Nixon pressed the button, there would have been a nuclear holocaust. ✓ b. If Nixon had pressed the button, the wire would have miraculously malfunctioned. ✗

37 / 40

Problem for Special Orderings?

Response part 1: closeness ordering need not correspond to intuitive ordering. Recall Fine (1975): (24) a. If Nixon pressed the button, there would have been a nuclear holocaust. ✓ b. If Nixon had pressed the button, the wire would have miraculously malfunctioned. ✗ Disaster for ordering semantics?

37 / 40

Problem for Special Orderings?

Response part 1: closeness ordering need not correspond to intuitive ordering. Recall Fine (1975): (24) a. If Nixon pressed the button, there would have been a nuclear holocaust. ✓ b. If Nixon had pressed the button, the wire would have miraculously malfunctioned. ✗ Disaster for ordering semantics? Lewis (1979): weight violations of law more than disparities in

• ther facts.

37 / 40

Problem for Special Orderings?

Response part 1: closeness ordering need not correspond to intuitive ordering. Recall Fine (1975): (24) a. If Nixon pressed the button, there would have been a nuclear holocaust. ✓ b. If Nixon had pressed the button, the wire would have miraculously malfunctioned. ✗ Disaster for ordering semantics? Lewis (1979): weight violations of law more than disparities in

• ther facts.

We still need a theory of the closeness ordering that predicts special orderings in the right cases, but nothing has ruled this

• ut yet.

37 / 40

Problem for Special Orderings?

Response part 2: actually, the high reading account needs special orderings too.

38 / 40

Problem for Special Orderings?

Response part 2: actually, the high reading account needs special orderings too. (25) Scenario: Cory, who is donkeyless, is a bit crazy. He’s disposed to take out his anger on his most prized

• possession. He also took part in the game show

described in (21), but also lost in the first round. Had he won any rounds, the prize from the most advanced round he won would have become his prized possession, and he would have beaten it, but he wouldn’t beat anything else. Now consider the following. (26) If Cory owned a donkey, he would beat it.

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Problem for Special Orderings?

Response part 2: actually, the high reading account needs special orderings too. (25) Scenario: Cory, who is donkeyless, is a bit crazy. He’s disposed to take out his anger on his most prized

• possession. He also took part in the game show

described in (21), but also lost in the first round. Had he won any rounds, the prize from the most advanced round he won would have become his prized possession, and he would have beaten it, but he wouldn’t beat anything else. Now consider the following. (26) If Cory owned a donkey, he would beat it. In this scenario, the salient reading of (26) seems false. If Cory had owned Eeyore, he would own but not beat Herbert.

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Problem for Special Orderings?

To get this right, the high reading account needs the worlds where Cory wins 2 or 3 donkeys to be as close as the one where he wins 1. It needs a special ordering. But then we can get the right results from the special ordering alone, without the high reading.

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Overview

Accounting for the Old Data Ordering Semantics + Dynamic Binding Route 1: Special Orderings Route 2: High Readings Returning to the New Data The Problem for High Readings The Success of Special Orderings Some Objections and Replies Saving High Readings? Problem for Special Orderings? Takeaway

Takeaway

Counterfactual donkey sentences have universal entailments, but not of the sort we’d expect from high reading accounts. The special ordering account seems to get things right. But we still need a theory of how these orderings arise.

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Thanks!

References

Fine, Kit (1975). “Critical Notice of David Lewis’s Counterfactuals”. In: Mind 84, pp. 451–458. Groenendijk, Jeroen and Martin Stokhof (1991). “Dynamic Predicate Logic”. In: Linguistics and Philosophy 14, pp. 39–100. Groenendijk, Jeroen, Martin Stokhof, and Frank Veltman (1996). “Coreference and Modality”. In: The Handbook of Contemporary Semantic Theory. Ed. by Shalom Lappin. Blackwell, pp. 179–213. Lewis, David (1979). “Counterfactual Dependence and Time’s Arrow”. In: Noˆ us 13, pp. 455–476. Van Rooij, Robert (2006). “Free choice counterfactual donkeys”. In: Journal of Semantics 23.4, pp. 383–402. Walker, Andreas and Maribel Romero (2015). “Counterfactual donkey sentences: A strict conditional analysis”. In: Proceedings of SALT 25, pp. 288–307. Wang, Yingying (2009). “Counterfactual donkey sentences: a response to Robert van Rooij”. In: Journal of Semantics 26.3,

• pp. 317–328.